Amy said 49 of her teammates got hits during a recent softball game. Which decimal represents this same amount?

Write expression as a sine or cosine of an angle.<br>cos 94° cos 18° + sin 94° sin 18°

MArishka [77]

<h3>Answer: cos(76)</h3>

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Explanation:

The original expression is of the pattern cos cos + sin sin. This pattern matches the second identity in the hint. Specifically, we'll say the following:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

cos(A)cos(B) + sin(A)sin(B) = cos(A - B)

cos(94)cos(18) + sin(94)sin(18) = cos(94 - 18)

cos(94)cos(18) + sin(94)sin(18) = cos(76)

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We can verify this by use of a calculator. Make sure your calculator is in degree mode.

cos(94)cos(18) + sin(94)sin(18) = 0.24192
cos(76) = 0.24192

Both expressions give the same decimal approximation, so this helps confirm the two expressions are equal. You could also use the idea that if x = y, then x-y = 0. Through this method, you'll subtract the left and right hand sides and you should get (very close to) zero.

6 0

3 years ago

I have to write the number 12.873 in words

Nina [5.8K]

Twelve and eight hundred seventy three thousandths

7 0

3 years ago

HURRRY PLEASE ANSWER I ONLY HAVE 5 MINN which expressions are equivalent to - 72 + (-6.5) + 2.5z + 4y - 1.5

STALIN [3.7K]

Answer:

fghwjklpkjqkhb cghdbhn bwn x wxhw hwbmx

Step-by-step explanation:

8 0

3 years ago

4^n + 1 , Where n is a natural number , will

antiseptic1488 [7]

Answer:

a) will definitely be an odd number

Step-by-step explanation:

4^n is always even (when you multiply even and even number, the product is always even)

when you add one to even number, the sum is always odd

so 4^n +1 is odd.

5 0

3 years ago

Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the ra

bearhunter [10]

Answer:

$\frac{dh}{dt}=-\frac{1}{2\pi}cm/min$

Step-by-step explanation:

From similar triangles, see diagram in attachment

$\frac{r}{4}=\frac{h}{16}$

We solve for $r$ to obtain,

$r=\frac{h}{4}$

The formula for calculating the volume of a cone is

$V=\frac{1}{3}\pi r^2h$

We substitute the value of $r=\frac{h}{4}$ to obtain,

$V=\frac{1}{3}\pi (\frac{h}{4})^2h$

This implies that,

$V=\frac{1}{48}\pi h^3$

We now differentiate both sides with respect to $t$ to get,

$\frac{dV}{dt}=\frac{\pi}{16}h^2 \frac{dh}{dt}$

We were given that water is drained out of the tank at a rate of $2cm^3/min$

This implies that $\frac{dV}{dt}=-2cm^3/min$ .

Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means $h=8cm$ .

We substitute this values to obtain,

$-2=\frac{\pi}{16}(8)^2 \frac{dh}{dt}$

$\Rightarrow -2=4\pi \frac{dh}{dt}$

$\Rightarrow -1=2\pi \frac{dh}{dt}$

$\frac{dh}{dt}=-\frac{1}{2\pi}$

3 0

4 years ago

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