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3 years ago

What is 60% of 125 enter answer

Mathematics

2 answers:

Finger [1]3 years ago

8 0

It’s 75 because 125 x0.60 = 75

erastovalidia [21]3 years ago

6 0

60% of 125 is 75.....

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Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) + sin(2t),[0, π/2].

castortr0y [4]

Answer:

The absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0.$

Step-by-step explanation:

Differentiate of $f$ both sides w.r.t. $t$ ,

$f(t)=2 \cos t+\sin 2t$

$\Rightarrow f'(t)=-2\sin t+2\cos 2t$

Now take $f'(t)=0$

$\Rightarrow -2\sin t+2\cos 2t=0$

$\Rightarrow 2\cos 2t=2\sin t$

$\Rightarrow \cos 2t=\sin t$

$\Rightarrow 1-2\sin ^2t =\sin t \quad \quad [\because \cos 2t = 1-2\sin ^2t]$

$\Rightarrow 2\sin ^2t+\sin t-1=0$

$\Rightarrow 2\sin ^2t+2\sin t-\sin t-1=0$

$\Rightarrow 2\sin t(\sin t+1)-1(\sin t+1)=0$

$\Rightarrow (\sin t+1)(2\sin t-1)=0$

$\Rightarrow \sin t+1=0 \;\text{and}\; 2\sin t-1=0$

$\Rightarrow \sin t =-1 \;\text{and}\; \sin t =\frac 12$

In the interval $0\leq t\leq \frac {\pi}2$ , the answer to this problem is $\frac {\pi}6$

Now find the second derivative of $f(t)$ w.r.t. $t$ ,

$f''(t)=-2\cos t-4\sin 2t$

$\Rightarrow \left[f''(t)\right]_{t=\frac {\pi}6}=-2\times \frac {\sqrt 3}2-4\times \frac{\sqrt 3}2=-3\sqrt 3$

Thus, $f(t)$ is maximum at $t=\frac {\pi}6$ and minimum at $t=0$

$\left[f(t)\right]_{t=\frac {\pi}6}=2\times \frac {\sqrt 3}2+\frac{\sqrt 3}2=\frac{3\sqrt 3}2\;\text{and}\;\left[f(t)\right]_{t=\frac{\pi}2}= 2\times 0+0=0$

Hence, the absolute maximum is $\frac{3\sqrt 3}2$ and the absolute minimum value is $0$ .

7 0

3 years ago

Find the solution to the system of linear equations y = 5x + 4 and y = −3x + 12 using the intersection method. Check your answer

Umnica [9.8K]

Answer:

The solution to the system of linear equations is (1,9).

Step-by-step explanation:

The given system of linear equations

$y=5x+4$ ... (1)

$y=-3x+12$ .... (2)

Subtract equation (2) from equation (1) to eliminate y.

$y-y=(5x+4)-(-3x+12)$

$0=5x+4+3x-12$

On combining like terms, we get

$0=(5x+3x)+(4-12)$

$0=8x-8$

Add 8 on both sides.

$0+8=8x-8+8$

$8=8x$

Divide both sides by 8.

$1=x$

The value of x is 1.

Substitute x=1 in equation (1).

$y=5(1)+4$

$y=5+4$

$y=9$

The value of y is 9.

Therefore the solution to the system of linear equations is (1,9).

4 0

3 years ago

Find the sum of these polynomials

Nuetrik [128]

Hi there! The answer is B.

$( {x}^{2} - x + 7) + (9 {x}^{2} + 6)$
First we work out the parenthesis, which is easy because we can just remove them.

${x}^{2} - x + 7 + 9 {x}^{2} + 6$
Now rearrange our expression (in order to collect terms later).

${x}^{2} + 9 {x}^{2} - x + 7 + 6$
Next up is collecting the terms.

$10 {x}^{2} - x + 13$
The answer is B.

~ Hope this helps you!

7 0

3 years ago

Solve: x^2+4x-15<br><br> you don’t need to show steps

Veseljchak [2.6K]

Answer:

-2 ± √19

Explanation:

Quadratic formula

Hope this helps!

7 0

2 years ago

Find the surface area of a square based pyramid if the edge of the base is 8 inches and the slant height is 20 inches.

Sliva [168]

Answer:

384 Square Inches

Step-by-step explanation:

Given a square pyramid with base side edge and slant height

$\text{Surface Area} = A+\dfrac12 ps, where:\\A=$Area of Base\\p=Perimeter of base\\s=Slant Height$

In the given pyramid:

Slant Height=20 inches
Base Edge = 8 Inches

Therefore:

Area of Base, A =8 X 8 =64 Square Inches

Perimeter of base, p =4 X 8 =32 Inches

$\text{Surface Area} = 64+\dfrac12 *32*20\\=64+320\\=384$ Square Inches$

7 0

4 years ago

What is 60% of 125 enter answer​

What is 60% of 125 enter answer