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3 years ago

Find the indicated limit, if it exists.(7 points)

Mathematics

1 answer:

Alecsey [184]3 years ago

7 0

Answer:

Step-by-step explanation:

The left hand limit is when we approach zero from left. We use the function on this domain in finding the limit.

$\lim_{x \to 0^-} f(x)=7-x^2$

$\lim_{x \to 0^-} f(x)=7-(0)^2=7$

The right hand limit is

$\lim_{x \to 0^+} f(x)=10x+7$

$\lim_{x \to 0^+} f(x)=10(0)+7=7$

Since the left hand limit equals the right hand limit;

$\lim_{x \to 0} f(x)=7$

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What were the lengths of the legs of a right triangle in which measures 19 degrees and the hypotenuses 15 units long

Otrada [13]

Answer:

The legs of a triangle with a hypotenuse that measures 15 units long have lengths that are equal to 15 times the sine or cosine of the given angle.

leg 1 = (15 units) x (cos 19) = 14.18 units

leg 2 = (15 units) x (sin 19) = 4.88 units

The lengths of the legs are 14.18 units and 4.88 units.

8 0

3 years ago

The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lenghts of the bases of

Sati [7]

Answer:

<h2>The lengths of the bases of the trapezoid:</h2><h2>42/h cm and 84/h cm.</h2>

Step-by-step explanation:

The formula of an area of a triangle:

$A=\dfrac{bh}{2}$

b - base

h - height

We have b = 21cm, h = 6cm.

Substitute:

$A=\dfrac{(21)(6)}{2}=63\ cm^2$

The formula of an area of a trapezoid:

$A=\dfrac{b_1+b_2}{2}\cdot h$

b₁, b₂ - bases

h - height

We have b₁ = 2b₂, therefore b₁ + b₂ = 2b₂ + b₂ = 3b₂.

The area of a triangle and the area of a trapezoid are the same.

Therefore

$\dfrac{3b_2}{2}\cdot h=63$ multiply both sides by 2

$3b_2h=126$ divide both sides by 3

$b_2h=42$ divide both sides by h

$b_2=\dfrac{42}{h}$

$b_1=2b_2\to b_1=2\cdot\dfrac{42}{h}=\dfrac{84}{h}$

8 0

3 years ago

Read 2 more answers

Alisha hiked a trail that was 9/10 mile and Joseph hiked a trail that was 5/10 mile. How much farther did Alisha hike than Josep

Elenna [48]

Answer:

4/10 or 2/5 of a mile more.

Step-by-step explanation:

Since the denominators are the same, all you have to do is subtract the numerators.

9-5=10.

Therefore, Alisha hiked 2/5 of a mile further than Joseph.

8 0

3 years ago

The area of a trapezoid is 33 square meters. one base is 4 meters long and the other base is 7 meters. find the height of the tr

In-s [12.5K]

h=6
A=((a=b)/2)h
33=((4+7)/2)h
33=(11/2)h
33=5.5h
6=h

7 0

3 years ago

Can someone please help me :)

gavmur [86]

Answer:

90 degree

Step-by-step explanation:

Three points A, B, and C are added and shown in attached picture.

As the property of inscribed angle in circle:

angle BAC = (1/2) x 88 = 44 deg

As the property of complement angle:

angle ABC = 180 - 89 = 91 deg

As the property of sum of three angles in a triangle:

angle ACB + angle ABC + angle BAC = 180 deg

=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg

One more time, we use the property of inscribed angle in circle:

x = 2 x angle ACB = 2 x 45 = 90 deg

Hope this helps!

7 0

3 years ago