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matrenka [14]
3 years ago
13

What is the Y-intercept in the equation y= 4x -4?

Mathematics
1 answer:
GrogVix [38]3 years ago
8 0

Answer:

The y-intercept is -4

Step-by-step explanation:

You have your x intercept, which is 4 and your y is -4. Hope this helps :)

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Evaluate the integral. (Use C for the constant of integration.) <br> cos(x) (8 + 7 sin^2(x)) dx
UNO [17]

Answer: 8 \sin x +7(\dfrac{\sin^3x}{3})+C

Step-by-step explanation:

Consider \int \cos(x) (8+7 \sin^2(x)) \, dx

Substitute  t= sinx

then dt = cos x dx

\int \cos(x) (8+7 \sin^2(x)) \, dx = \int (8+7t^2)dt\\\\ =8t+7(\dfrac{t^3}{3})+C

[\int x^ndx=\dfrac{x^{n+1}}{n+1}+C]

=8 \sin x +7(\dfrac{\sin^3x}{3})+C

Hence, \int \cos(x) (8+7 \sin^2(x)) \, dx=8 \sin x +7(\dfrac{\sin^3x}{3})+C

5 0
3 years ago
Solve for x. Round to the nearest tenth,if necessary
cupoosta [38]

Answer:

x = 83.7 units

Step-by-step explanation:

  • given adjacent: 56, given angle: 48°, asked to find hypotenuse, x?

Using cosine rule:

→ adjacent/hypotenuse = cos(∅)

→ 56/hypotenuse = cos(48)

→ hypotenuse = 56/cos(48)

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8 0
2 years ago
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A bacteria population grows by 10% every 2 years. Presently, the population is 80 000 bacteria. Find the population 12 years ago
Sever21 [200]

In this problem

we have an exponential growth function of the form

y=a(1+r)^{\frac{t}{2}}

where

r=10%=0.10

Let

t=0 ---------> 12 years ago

so

Presently -------> t=12 years, y=80,000 bacteria

substitute

\begin{gathered} 80,000=a(1+0.10)^{\frac{12}{2}} \\ a=\frac{80,000}{1.10^6} \\  \\ a=45,158\text{ bacteria} \end{gathered}

therefore

<h2>The population 12 years ago was 45,158 bacteria</h2>
6 0
1 year ago
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