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3 years ago

Explain how the math drawing can help you solve 8+ =14

Mathematics

2 answers:

12345 [234]3 years ago

7 0

They help by the number of total dots on the diagram, they told you the answer to 8+6=14

Sloan [31]3 years ago

3 0

Answer:

Step-by-step explanation:

We are given that 8+_=14

We have to explain how that math drawing can help to solve 8+_=14.

We draw two circles in which one contain 8 particles and other contain 14 particles.

In firs circle, number of particles =8

Difference between particles of two given circles =14-8=6

In second circle, there are 14 particles which are increase by 6 particles in first circle have 8 particles.

Hence, 8+6=14

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A computer can sort x objects in t seconds, as modeled by the function

r-ruslan [8.4K]

Answer:

36 objects

Step-by-step explanation:

You want the value of x when t=9, so you're solving ...

9 = 0.007x^2 +0.003x

9 = 0.007(x^2 + 3/7x)

From here, we observe that an approximation is probably sufficient.

9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2

x ≈ 3/√.007 ≈ 35.9 ≈ 36

We can check:

.007(36)(36 3/7) = 9.18

.007(35)(35 3/7) = 8.68

To keep the computer busy for 9 seconds, it needs to sort 36 objects.

6 0

3 years ago

CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is

Rufina [12.5K]

Answer:

$\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}$

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

$y=\sin(x)\cos(x)$

Take the derivative of both sides with respect to x:

$\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]$

We need to use the product rule:

$(uv)'=u'v+uv'$

So, differentiate:

$y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]$

Evaluate:

$y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))$

Simplify:

$y'=\cos^2(x)-\sin^2(x)$

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

$0=\cos^2(x)-\sin^2(x)$

Now, let's solve for x. First, we can use the difference of two squares to obtain:

$0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))$

Zero Product Property:

$0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)$

Solve for each case.

Case 1:

$0=\cos(x)-\sin(x)$

Add sin(x) to both sides:

$\cos(x)=\sin(x)$

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

$0=\cos(x)+\sin(x)$

Subtract sine from both sides:

$\cos(x)=-\sin(x)$

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

$\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}$

And we're done!

Edit: Small Mistake :)

5 0

3 years ago

Can someone solve this?

ladessa [460]

First question:

Recall that $\cos^2x+\sin^2x=1$ and $\sqrt{x^2}=|x|$ for all $x$ . So

$\sqrt{1-\cos^2x}=\sqrt{\sin^2x}=|\sin x|$

$\sqrt{1-\sin^2x}=\sqrt{\cos^2x}=|\cos x|$

For $0$ , we expect both $\cos x>0$ and $\sin x>0$ (i.e. the sine and cosine of any angle that lies in the first quadrant must be positive). By definition of absolute value, $|x|=x$ if $x>0$ .

So we have

$\dfrac{\sqrt{1-\cos^2x}}{\sin x}+\dfrac{\sqrt{1-\sin^2x}}{\cos x}=\dfrac{\sin x}{\sin x}+\dfrac{\cos x}{\cos x}=1+1=\boxed{2}$

making H the answer.

Second question:

C is always true, because the inequality reduces to x > y.

6 0

4 years ago

What is the gcf of 27 and 36

mestny [16]

The answer would be 9. 9x3=27 and 9x4=36. Although 3 fits into both, 9 is the BIGGER number that also fits into both of the numbers shown in the problem.

5 0

3 years ago

Read 2 more answers

Find the angle of XYZ give your answer to 1 decimal place

miskamm [114]

Answer:

66.4°

Step-by-step explanation:

To find the angle XYZ, we are to use sine rule. For this, we have to first find ∠Z.

Given that: ∠X = 90° (right angle), XY = 6 cm, YZ = 15 cm. Hence:

$\frac{sin(Z)}{XY}=\frac{sin(X)}{YZ}\\\\Substituting:\\\\\frac{sin(Z)}{6} =\frac{sin(90)}{15} \\\\sin(Z)=\frac{sin(90)*6}{15}\\\\sin(Z)=0.4\\\\Z=sin^{-1}(0.4)\\\\Z=23.6^o$

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

90 + ∠Y + 23.6 = 180

113.6 + ∠Y = 180

∠Y = 180 - 113.6

∠Y = 66.4°

∠Y = ∠XYZ = 66.4°

3 0

3 years ago